Effects of surface roughness on the drag coefficient of finite-span cylinders freely rolling on an inclined plane

Abstract

We present an experimental investigation aimed at understanding the effects of surface roughness on the time-mean drag coefficient ( $\bar {C}_{D}$ ) of finite-span cylinders ( $\text {span/diameter} = \text {aspect ratio}$ , $0.51 \le AR \le 6.02$ ) freely rolling without slip on an inclined plane. While lubrication theory predicts an infinite drag force for ideally smooth cylinders in contact with a smooth surface, experiments yield finite drag coefficients. We propose that surface roughness introduces an effective gap ( $G_{eff}$ ) resulting in a finite drag force while allowing physical contact between the cylinder and the plane. This study combines measurements of surface roughness for both the cylinder and the plane panel to determine a total relative roughness ( $\xi$ ) that can effectively describe $G_{eff}$ at the point of contact. It is observed that the measured $\bar {C}_{D}$ increases as $\xi$ decreases, aligning with predictions of lubrication theory. Furthermore, the measured $\bar {C}_{D}$ approximately matches combined analytical and numerical predictions for a smooth cylinder and plane when the imposed gap is approximately equal to the mean peak roughness ( $R_p$ ) for rough cylinders, and one standard deviation peak roughness ( $R_{p, 1\sigma }$ ) for relatively smooth cylinders. As the time-mean Reynolds number ( $\overline {Re}$ ) increases, the influence of surface roughness on $\bar {C}_{D}$ decreases, indicating that wake drag becomes dominant at higher $\overline {Re}$ . The cylinder aspect ratio ( $AR$ ) is found to have only a minor effect on $\bar {C}_{D}$ . Flow visualisations are also conducted to identify critical flow transitions and these are compared with visualisations previously obtained numerically. Variations in $\xi$ have little effect on the cylinder wake. Instead, $AR$ was observed to have a more pronounced effect on the flow structures observed. The Strouhal number ( $St$ ) associated with the cylinder wake shedding was observed to increase with $\overline {Re}$ , while demonstrating little dependence on $AR$ .